Role of the fission in the rprocess nucleosynthesis

Role of the fission in the r-process nucleosynthesis - Needed input Aleksandra Kelić and Karl-Heinz Schmidt GSI-Darmstadt, Germany • • What is the needed input? Mass and charge division in fission Saddle-point masses Conclusions

r-process and fission Trans. U elements ? 1) r-process endpoint ? Fission cycling ? 2) 3, 4) Ø Astrophysical conditions? Ø Characteristics of the fission process? 1) Cowan et al, Phys. Rep. 208 (1991) 267 2) Panov et al. , NPA 747 (2005) 633 3) Seeger et al, APJ 11 Suppl. (1965) S 121 4) Rauscher et al, APJ 429 (1994) 49 Aleksandra Kelić (GSI) NPA 3 – Dresden, 30. 03. 2007

Fission process Fission corresponds to a large-scale collective motion: Both static (e. g. potential) and dynamic (e. g. viscosity) properties play important role. At low excitation energies: influence of shell effects and pairing correlations. Aleksandra Kelić (GSI) NPA 3 – Dresden, 30. 03. 2007

What do we need? Fission competition in de-excitation of excited nuclei E* • Fission barriers • Fragment distributions • Level densities (pairing, shell corrections, symmetry classes) • Nuclear viscosity • Particle-emission widths Aleksandra Kelić (GSI) NPA 3 – Dresden, 30. 03. 2007

Source of information Estimated beam intensities at the future FAIR facility (K. -H. Schmidt et al) 82 50 82 28 20 50 20 2 28 8 - No experimental information - Relay on theory and model calculations Aleksandra Kelić (GSI) NPA 3 – Dresden, 30. 03. 2007

Mass and charge division in fission

Experimental information - Low energy • Particle-induced fission of long-lived targets and spontaneous fission: - A(E*) in most cases - A and Z distributions of light fission group only in thermalneutron induced fission on the stable targets • EM fission of secondary beams at GSI: - Z distributions at "one" energy Aleksandra Kelić (GSI) NPA 3 – Dresden, 30. 03. 2007

Basic idea Experimental survey at GSI by use of secondary beams K. -H. Schmidt et al. , NPA 665 (2000) 221 - Transition from single-humped to double-humped explained by macroscopic and microscopic properties of the potential-energy landscape near outer saddle. Aleksandra Kelić (GSI) NPA 3 – Dresden, 30. 03. 2007

Basic assumptions Macroscopic part: Given by properties of fissioning nucleus • Potential near saddle from exp. mass distributions at high E* (1): Microscopic part: Shells near outer saddle "resemble" shells of final fragments (but weaker) • Properties of shells from exp. nuclide distributions at low E* Dynamics: Approximations based on Langevin calculations • Mass asymmetry: decision near outer saddle • N/Z: decision near scission (3): Population of available states: With statistical weight (near saddle or scission) Rusanov et al, Phys. At. Nucl. 60 (1997) 683 (1) Maruhn and Greiner, PRL 32 (1974) 548; Pashkevich, NPA 477 (1988) 1; (3) P. Nadtochy, private communiation (2) Aleksandra Kelić (GSI) (2) N 88 N 82 Pashkevich et al. NPA 3 – Dresden, 30. 03. 2007

Macroscopic-microscopic approach Model parameters: • Curvatures, strengths and positions of two microscopic contributions as free parameters • These 6 parameters are deduced from the experimental fragment distributions and kept fixed for all systems and energies. N 82 N 88 Aleksandra Kelić (GSI) For each fission fragment we get: • Mass • Nuclear charge • Kinetic energy • Excitation energy • Number of emitted particles NPA 3 – Dresden, 30. 03. 2007

Comparison with EM data Fission of secondary beams after the EM excitation: black - experiment 92 U red - calculations 91 Pa 142 140 141 90 Th 138 89 Ac 131 132 Aleksandra Kelić (GSI) 133 134 135 136 137 139 With one and same set of model parameters for all systems NPA 3 – Dresden, 30. 03. 2007

Neutron-induced fission of 238 U for En = 1. 2 to 5. 8 Me. V Data - F. Vives et al, Nucl. Phys. A 662 (2000) 63; Aleksandra Kelić (GSI) Lines - Model calculations NPA 3 – Dresden, 30. 03. 2007

Applications in astrophysics Usually one assumes: a) symmetric split: AF 1 = AF 2 b) 132 Sn shell plays a role: AF 1 = 132, AF 2 = ACN - 132 Be careful: 260 U 276 Fm 300 U Deatailed r-process network calculations: N. Zinner (Aarhus) and G. Martinez-Pinedo (GSI) Aleksandra Kelić (GSI) NPA 3 – Dresden, 30. 03. 2007

Saddle-point masses

Fission barriers - Experimental information Relative uncertainty: >10 -2 Available data on fission barriers, Z ≥ 80 (RIPL-2 library) Aleksandra Kelić (GSI) NPA 3 – Dresden, 30. 03. 2007

Fission barriers - Experimental information Fission barriers Relative uncertainty: >10 -2 GS masses Relative uncertainty: 10 -4 - 10 -9 Courtesy of C. Scheidenberger (GSI) Aleksandra Kelić (GSI) NPA 3 – Dresden, 30. 03. 2007

Open problem Limited experimental information on the height of the fission barrier Neutron-induced fission rates for U isotopes Aleksandra Kelić (GSI) Panov et al. , NPA 747 (2005) NPA 3 – Dresden, 30. 03. 2007

Idea Predictions of theoretical models are examined by means of a detailed analysis of the isotopic trends of saddle-point masses. Experimental saddle-point mass Macroscopic saddle-point mass Usad Empirical saddle-point shellcorrection energy Aleksandra Kelić (GSI) NPA 3 – Dresden, 30. 03. 2007

Idea What do we know about saddle-point shell-correction energy? 1. Shell corrections have local character 2. Shell-correction energy at SP should be very small (e. g Myers and Swiatecki PRC 60 (1999); Siwek-Wilczynska and Skwira, PRC 72 (2005)) SCE ic! t y r ma e V he sc 1 -2 Me. V Neutron number If an model is realistic Slope of Usad as function of N should be ~ 0 Any general trend would indicate shortcomings of the macroscopic model. Aleksandra Kelić (GSI) NPA 3 – Dresden, 30. 03. 2007

Studied models 1. ) Droplet model (DM) [Myers 1977], which is a basis of often used results of the Howard-Möller fission-barrier calculations [Howard&Möller 1980] 2. ) Finite-range liquid drop model (FRLDM) [Sierk 1986, Möller et al 1995] 3. ) Thomas-Fermi model (TF) [Myers&Swiatecki 1996, 1999] 4. ) Extended Thomas-Fermi model (ETF) [Mamdouh et al. 2001] W. D. Myers, „Droplet Model of Atomic Nuclei“, 1977 IFI/Plenum W. M. Howard and P. Möller, ADNDT 25 (1980) 219. A. Sierk, PRC 33 (1986) 2039. P. Möller et al, ADNDT 59 (1995) 185. W. D. Myers and W. J. Swiatecki, NPA 601( 1996) 141 W. D. Myers and W. J. Swiatecki, PRC 60 (1999) 0 14606 -1 A. Mamdouh et al, NPA 679 (2001) 337 Aleksandra Kelić (GSI) NPA 3 – Dresden, 30. 03. 2007

Example for uranium Usad as a function of a neutron number A realistic macroscopic model should give a zero slope! Kelić and Schmidt, PLB 643 (2006) Aleksandra Kelić (GSI) NPA 3 – Dresden, 30. 03. 2007

Results Slopes of δUsad as a function of the neutron excess The most realistic macroscopic models: the TF model and the FRLD model Further efforts needed for the saddle-point mass predictions of the droplet model and the extended Thomas-Fermi model Kelić and Schmidt, PLB 643 (2006) Aleksandra Kelić (GSI) NPA 3 – Dresden, 30. 03. 2007

Conclusions - Good description of mass and charge division in fission based on a macroscopic-microscopic approach, which allows for robust extrapolations. Inclusion in r-process network calculations by N. Zinner (Aarhus) and G. Martinez-Pinedo (GSI). - According to a detailed analysis of the isotopic trends of saddlepoint masses indications have been found that the Thomas-Fermi model and the FRLDM model give the most realistic extrapolations in regions where no experimental data are available. - Need for more precise and new experimental data using new techniques and methods basis for further developments in theory. Aleksandra Kelić (GSI) NPA 3 – Dresden, 30. 03. 2007

Additional slides

Macroscopic-microscopic approach - Transition from single-humped to double-humped explained by macroscopic and microscopic properties of the potential-energy landscape near outer saddle. Macroscopic part: property of CN Microscopic part: properties of fragments* N 90 N 82 * Maruhn and Greiner, Z. Phys. 251 (1972) 431, PRL 32 (1974) 548; Pashkevich, NPA 477 (1988) 1;

Comparison with data - spontaneous fission Experiment Calculations (experimental resolution not included)

Comparison with data nth + Mass distribution 235 U (Lang et al. ) Charge distribution Z

Experiment - Difficulties • Experimental sources: Energy-dependent fission probabilities • Extraction of barrier parameters: Requires assumptions on level densities Gavron et al. , PRC 13 (1976) 2374

Ternary fission less than 1% of a binary fission Open symbols experiment Full symbols theory Rubchenya and Yavshits, Z. Phys. A 329 (1988) 217

Applications in astrophysics - first step Mass and charge distributions in neutrino-induced fission of r-process progenitors Phys. Lett. B 616 (2005) 48